Electrical prism: a high quality factor filter for millimeter-wave and terahertz frequencies

Abstract

Filters and methods which may be used with millimeter-wave and terahertz frequency range are disclosed. The filter is formed as an electrical prism which may include a first lattice forming an interface with a second lattice. Each lattice may include a plurality of passive elements, such as inductors, capacitors, and the like. The first lattice may include an input disposed at an input boundary thereof, while the second lattice may include an output disposed at an output boundary thereof. Furthermore, the first and second lattices may be configured to receive a signal at the input of the first lattice, propagate the signal to the interface, and direct the signal to the outputs of the second lattice.

What is claimed is: 
     
       1. A filter, comprising:
 a first lattice of inductors and capacitors having at least one input disposed at an input boundary thereof; and 
 a second lattice of inductors and capacitors having a plurality of outputs disposed at an output boundary thereof, the second lattice being configured to form an interface with the first lattice, the first and second lattices being configured to receive a signal at the input of the first lattice, propagate the signal to the interface, and direct the signal to the outputs of the second lattice, the output boundary being configured to compensate for differences in signal attenuation at the outputs. 
 
     
     
       2. The filter of  claim 1 , wherein the inductors of each lattice are serially and linearly disposed within a plane of the respective lattice and disposed along two or more directions so as to intersect at a plurality of intersections, and the capacitors are disposed at the intersections and coupled between the respective intersections and ground. 
     
     
       3. The filter of  claim 1 , wherein each output is associated with a different frequency of the signal. 
     
     
       4. The filter of  claim 1  having a factor F=L 2 C 2 /L 1 C 1  of no more than 10, wherein L 1  is an inductance of an inductor in the first lattice, L 2  is an inductance of an inductor in the second lattice, C 1  is a capacitance of a capacitor in the first lattice, and C 2  is a capacitance of a capacitor in the second lattice. 
     
     
       5. The filter of  claim 1 , wherein the output boundary is angled such that, for signals of higher frequencies, a travel distance from the interface to the respective output is reduced. 
     
     
       6. The filter of  claim 1 , wherein each of the first and second lattices is a rectangular lattice. 
     
     
       7. The filter of  claim 1 , wherein the first lattice is a rectangular lattice and the second lattice is a triangular lattice. 
     
     
       8. The filter of  claim 1 , wherein the interface forms a 45° angle with each of the first and second lattices. 
     
     
       9. The filter of  claim 1  further comprising a power divider disposed along the input boundary configured to generate a plurality of equi-phase sources from the signal received at the input of the first lattice. 
     
     
       10. The filter of  claim 1 , wherein the filter is implemented in a complementary metal-oxide semiconductor (CMOS) process. 
     
     
       11. A filter, comprising:
 at least one rectangular lattice of inductors and capacitors having at least one input disposed at an input boundary thereof; and 
 at least one triangular lattice of inductors and capacitors having a plurality of outputs disposed at an output boundary thereof, the output boundary being configured to compensate for differences in signal attenuation at the outputs, the triangular lattice being configured to form an interface with the rectangular lattice, the inductors of each lattice being serially and linearly disposed within a plane of the respective lattice and disposed along two or more directions so as to intersect at a plurality of intersections, each of the capacitors being disposed at the intersections and coupled between the respective intersection and ground, the rectangular and triangular lattices being configured to receive a signal at the input of the rectangular lattice, propagate the signal to the interface, and direct the signal to the outputs of the triangular lattice. 
 
     
     
       12. The filter of  claim 11 , wherein each output is associated with a different frequency of the signal. 
     
     
       13. The filter of  claim 11 , wherein the output boundary of the second lattice is angled such that, for signals of higher frequencies, a travel distance from the interface to the respective output is reduced. 
     
     
       14. The filter of  claim 11 , wherein the interface forms a 45° angle with each of the first and second lattices. 
     
     
       15. The filter of  claim 11  having a factor F=L 2 C 2 /L 1 C 1  of no more than 10, wherein L 1  is an inductance of an inductor in the rectangular lattice, L 2  is an inductance of an inductor in the triangular lattice, C 1  is a capacitance of a capacitor in the rectangular lattice, and C 2  is a capacitance of a capacitor in the triangular lattice. 
     
     
       16. The filter of  claim 11 , wherein the capacitors are metal-oxide semiconductor (MOS) capacitors. 
     
     
       17. The filter of  claim 11 , wherein each of the inputs and outputs includes a ground-signal-ground (GSG) pad. 
     
     
       18. The filter of  claim 11  further comprising a power divider disposed along the input boundary configured to generate a plurality of equi-phase sources from the signal received at the input of the first lattice. 
     
     
       19. The filter of  claim 11 , wherein the filter is implemented in a complementary metal-oxide semiconductor (CMOS) process. 
     
     
       20. A method for filtering signals, comprising the steps of:
 providing a rectangular lattice of inductors and capacitors having at least one input disposed at an input boundary thereof; 
 providing a triangular lattice of inductors and capacitors having a plurality of outputs disposed at an output boundary thereof, the output boundary being angled to compensate for differences in signal attenuation at the outputs; 
 forming an interface between the rectangular lattice and the triangular lattice; 
 providing a signal to the input of the rectangular lattice; 
 providing one or more equi-phase sources of the signal to be received by the rectangular lattice and propagated to the interface; and 
 directing the signal to the outputs of the triangular lattice such that higher frequency components of the signal propagate to outputs that are relatively closer to the interface.